Aiming at the difficulty of existing extended state observers in balancing the suppression capabilities for both periodic and aperiodic disturbances, particularly the insufficient observation and compensation accuracy for specific frequency harmonics caused by nonlinearities in voltage source inverters, a current harmonic suppression method based on a quasi-resonant extended state observer (QRESO) was proposed. By embedding a quasi-resonant controller into the extended state observer (ESO) architecture, a QRESO with both low-frequency disturbance observation and high-frequency harmonic suppression capabilities was constructed, and disturbance feedforward compensation was implemented within a model-free predictive current control framework. The proposed method can accurately extract 6th-order harmonic disturbances through the synergistic action of low-frequency integral and high-frequency resonant modules while maintaining system stability. Experimental results demonstrate that compared with traditional extended state observers, under dead time conditions of 1, 2 and 6 μs, the QRESO reduces the 6th-order harmonic of q-axis current by 95%, 97% and 97% respectively, while decreasing the 5th and 7th harmonics of phase current to below 1%, it significantly improves the current waveform quality and total harmonic distortion, verifying the superior performance of this method in improving current quality.